Nonlinear Analysis, Stochastic Processes, and Optimal Control in Functional Spaces
This community develops the mathematical frameworks for analyzing complex systems governed by partial differential equations, stochastic processes, and network dynamics, with a focus on existence, uniqueness, and control of solutions.
The work centers on the rigorous analysis of nonlinear partial differential equations, particularly reaction-diffusion systems and elliptic equations, within abstract functional settings such as Banach and Sobolev spaces. A significant portion of the research addresses stochastic differential equations and Brownian motion, applying large deviation principles to understand probabilistic behaviors. Additionally, the community investigates optimal control and optimal transport problems, often in the context of complex dynamical networks and fluid dynamics, including magneto-micropolar fluids. These mathematical tools are applied to solve inverse problems and analyze the stability of solutions in various measure-theoretic contexts.
The largest share of the community's output is found in radon research, accounting for 4.3% of all radon research, and 2,105 papers here.
The community comprises 21,515 papers, publishing most frequently in arXiv (Cornell University), the Pacific Journal of Mathematics, and the Transactions of the American Mathematical Society.
Recent work continues to focus on the convergence of non-symmetric forms, nonlinear rough Fokker–Planck equations, and the asymptotic behavior of eigenvalues in Toeplitz matrices, alongside studies on cluster synchronization in stochastic networks and critical Liouville quantum gravity.